The ESs then engage in P2P communications for cooperative consensus formation among their aggregated gradients. For this purpose, we assume that they exploit linear distributed consensus iterations [1]}, where during training round \(k\) , each ES \(m\in \mathcal {M}\)  conducts \(\phi ^{(k)}\in \mathbb {N}\) 
consensus rounds of P2P communications with its neighboring ESs.
During each round \(l=0,\cdots ,\phi ^{(k)}-1\)  of P2P communications, the evolution of the local gradient of ES \(m\in \mathcal {M}\)  can be expressed as:
\(\textbf {x}_{m}^{(l+1)}= \lambda ^{(k)}_{m,m} \textbf {x}_{m}^{(l)}+ \sum _{m^{\prime }\in \varrho (m)} \lambda ^{(k)}_{m,m^{\prime }}\textbf {x}_{m^{\prime }}^{(l)},\) 
